带内变量的热力学一致梯度弹性
Thermodynamically consistent gradient elasticity with an internal variable
摘要：
热力学在连续介质力学中的作用和正确本构关系的推导是理性力学的一个讨论主题。经典文献没有使用积累的热力学知识，对不可逆热力学的启发式方法非常挑剔。本文建立了考虑记忆效应和耗散效应的小应变梯度弹性理论。该方法是具有内变量的非平衡态热力学方法，因此，本构关系在构造上与热力学相容。引入了单张量内变量弹性体的热力学吉布斯关系。热力学势是一阶弱非局域势，并计算了熵产生。在此基础上，构造了本构函数和内变量的演化方程。第二定律分析表明梯度项对应力的贡献，也没有耗散。
英文摘要：
The role of thermodynamics in continuum mechanics and the derivation of the proper constitutive relations is a discussed subject of Rational Mechanics. The classical literature did not use the accumulated knowledge of thermostatics and was very critical with the heuristic methods of irreversible thermodynamics. In this paper, a small strain gradient elasticity theory is constructed with memory effects and dissipation. The method is nonequilibrium thermodynamics with internal variables; therefore, the constitutive relations are compatible with thermodynamics by construction. Thermostatic Gibbs relation is introduced for elastic bodies with a single tensorial internal variable. The thermodynamic potentials are first-order weakly nonlocal, and the entropy production is calculated. Then the constitutive functions and the evolution equation of the internal variable is constructed. The second law analysis has shown a contribution of gradient terms to the stress, also without dissipation.
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